Evaluating the Effects of Pore Tortuosity on the Propagation of Compressional Waves in Saturated Soils

In the wave theory of saturated soils, pore tortuosity is an important physical property for quantifying the added mass force caused by the relative acceleration between solid and liquid phases. However, this inertial force is often ignored for simplicity in practical applications. To investigate the influence of pore tortuosity on the propagation of compressional waves in saturated soils, a system of generalized governing equations for one-dimensional infinitesimal strain elastic waves is solved using the Laplace transform method. Semi-analytical solutions are obtained for the spatiotemporal distributions of the excess pore water pressure, the pore water velocity, and the soil particle velocity caused by a step load perturbation under undrained conditions. These solutions are used to evaluate the effects of pore tortuosity on the velocities and amplitudes of fast and slow compressional waves. The results show that pore tortuosity has an insignificant effect on the propagation of fast compressional waves, but for slow compressional waves, the larger the pore tortuosity is, the lower the wave velocity and the larger the wave amplitude. Ignoring the influence of pore tortuosity can lead to an underestimation of the arrival time of slow compressional wave. The propagation of this wave is limited to a distance of approximately 1 m away from the loading boundary. This research finding is purely theoretical. For further experimental validation, it is suggested to detect the slow compressional wave by placing miniature acoustic receiving transducers as close as possible to the loading or transmitting surface. The proposed solutions are also useful for calibrating sophisticated numerical codes for dynamic consolidation of saturated soils and wave transmission in porous media.